sfepy.solvers.nls module¶

Nonlinear solvers.

class sfepy.solvers.nls.Newton(conf, **kwargs)[source]¶

Solves a nonlinear system $f(x) = 0$ using the Newton method.

The solver uses a backtracking line-search on divergence.

Kind: ‘nls.newton’

For common configuration parameters, see Solver.

Specific configuration parameters:

Parameters:

i_maxint (default: 1): The maximum number of iterations.
eps_afloat (default: 1e-10): The absolute tolerance for the residual, i.e. $||f(x^i)||$ .
eps_rfloat (default: 1.0): The relative tolerance for the residual, i.e. $||f(x^i)|| / ||f(x^0)||$ .
eps_mode‘and’ or ‘or’ (default: ‘and’): The logical operator to use for combining the absolute and relative tolerances.
machepsfloat (default: 2.220446049250313e-16): The float considered to be machine “zero”.
lin_redfloat or None (default: 1.0): The linear system solution error should be smaller than (eps_a * lin_red), otherwise a warning is printed. If None, the check is skipped.
lin_precisionfloat or None: If not None, the linear system solution tolerances are set in each nonlinear iteration relative to the current residual norm by the lin_precision factor. Ignored for direct linear solvers.
step_red0.0 < float <= 1.0 (default: 1.0): Step reduction factor. Equivalent to the mixing parameter $a$ : $(1 - a) x + a (x + dx) = x + a dx$
ls_onfloat (default: 0.99999): Start the backtracking line-search by reducing the step, if $||f(x^i)|| / ||f(x^{i-1})||$ is larger than ls_on.
ls_red0.0 < float < 1.0 (default: 0.1): The step reduction factor in case of correct residual assembling.
ls_red_warp0.0 < float < 1.0 (default: 0.001): The step reduction factor in case of failed residual assembling (e.g. the “warp violation” error caused by a negative volume element resulting from too large deformations).
ls_min0.0 < float < 1.0 (default: 1e-05): The minimum step reduction factor.
give_up_warpbool (default: False): If True, abort on the “warp violation” error.
check0, 1 or 2 (default: 0): If >= 1, check the tangent matrix using finite differences. If 2, plot the resulting sparsity patterns.
deltafloat (default: 1e-06): If check >= 1, the finite difference matrix is taken as $A_{ij} = \frac{f_i(x_j + \delta) - f_i(x_j - \delta)}{2 \delta}$ .
logdict or None: If not None, log the convergence according to the configuration in the following form: {'text' : 'log.txt', 'plot' : 'log.pdf'}. Each of the dict items can be None.
is_linearbool (default: False): If True, the problem is considered to be linear.

__call__(vec_x0, conf=None, fun=None, fun_grad=None, lin_solver=None, iter_hook=None, status=None, **kwargs)[source]¶: Call self as a function.

__init__(conf, **kwargs)[source]¶

__module__ = 'sfepy.solvers.nls'¶

name = 'nls.newton'¶

class sfepy.solvers.nls.PETScNonlinearSolver(conf, pmtx=None, prhs=None, comm=None, **kwargs)[source]¶

Interface to PETSc SNES (Scalable Nonlinear Equations Solvers).

The solver supports parallel use with a given MPI communicator (see comm argument of PETScNonlinearSolver.__init__()). Returns a (global) PETSc solution vector instead of a (local) numpy array, when given a PETSc initial guess vector.

For parallel use, the fun and fun_grad callbacks should be provided by PETScParallelEvaluator.

Kind: ‘nls.petsc’

For common configuration parameters, see Solver.

Specific configuration parameters:

Parameters:

methodstr (default: ‘newtonls’): The SNES type.
i_maxint (default: 10): The maximum number of iterations.
if_maxint (default: 100): The maximum number of function evaluations.
eps_afloat (default: 1e-10): The absolute tolerance for the residual, i.e. $||f(x^i)||$ .
eps_rfloat (default: 1.0): The relative tolerance for the residual, i.e. $||f(x^i)|| / ||f(x^0)||$ .
eps_sfloat (default: 0.0): The convergence tolerance in terms of the norm of the change in the solution between steps, i.e. $||delta x|| < epsilon_s ||x||$

__call__(vec_x0, conf=None, fun=None, fun_grad=None, lin_solver=None, iter_hook=None, status=None, **kwargs)[source]¶: Call self as a function.

__init__(conf, pmtx=None, prhs=None, comm=None, **kwargs)[source]¶

__module__ = 'sfepy.solvers.nls'¶

name = 'nls.petsc'¶

class sfepy.solvers.nls.ScipyBroyden(conf, **kwargs)[source]¶

Interface to Broyden and Anderson solvers from scipy.optimize.

Kind: ‘nls.scipy_broyden_like’

For common configuration parameters, see Solver.

Specific configuration parameters:

Parameters:

methodstr (default: ‘anderson’): The name of the solver in scipy.optimize.
i_maxint (default: 10): The maximum number of iterations.
alphafloat (default: 0.9): See scipy.optimize.
Mfloat (default: 5): See scipy.optimize.
f_tolfloat (default: 1e-06): See scipy.optimize.
w0float (default: 0.1): See scipy.optimize.

__call__(vec_x0, conf=None, fun=None, fun_grad=None, lin_solver=None, iter_hook=None, status=None, **kwargs)[source]¶: Call self as a function.

__init__(conf, **kwargs)[source]¶

__module__ = 'sfepy.solvers.nls'¶

name = 'nls.scipy_broyden_like'¶

set_method(conf)[source]¶

sfepy.solvers.nls.check_tangent_matrix(conf, vec_x0, fun, fun_grad)[source]¶: Verify the correctness of the tangent matrix as computed by fun_grad() by comparing it with its finite difference approximation evaluated by repeatedly calling fun() with vec_x0 items perturbed by a small delta.

sfepy.solvers.nls.conv_test(conf, it, err, err0)[source]¶

Nonlinear solver convergence test.

Parameters:

confStruct instance: The nonlinear solver configuration.
itint: The current iteration.
errfloat: The current iteration error.
err0float: The initial error.

Returns:

statusint: The convergence status: -1 = no convergence (yet), 0 = solver converged - tolerances were met, 1 = max. number of iterations reached.

sfepy.solvers.nls.standard_nls_call(call)[source]¶: Decorator handling argument preparation and timing for nonlinear solvers.